Is there a way on the back of a check that was deposited at an ATM to know which of the numbers stamped on the back of the check is the Terminal ID # so we can track down where a deposit was made via an ATM deposit?

Whether any of those numbers represent the terminal number will depend on who processed the checks. There is no standard that I am aware of addressing the matter, and it's possible the terminal number is not represented at all. The other complication is the fact that terminal numbers are assigned by either the ATM deployer or the party controlling the ATM. There's no standard format for the terminal number assignments, and there's a good possibility that two or more controllers or deployers will use the same number.

I'd suggest trying to determine the depositary bank (the bank that first processed the check) and contact it to get information on the actual machine involved.

Thanks John.